Lena is polishing a helper function for the company’s automated document delivery system to help it navigate the office floor. Mark pointed out that the robot occasionally gets stuck because it doesn't account for temporary blockages like wet floor signs or moved furniture. She needs to calculate the total number of clear paths the robot can take from the entrance to the mailroom, assuming it only moves forward or downward across the floor grid. For example, if a small 3x3 office layout has a single blocked desk right in the middle, the robot should identify that there are exactly two unique ways to reach the destination by skirting around the obstacle.